Inspired in equal part by fast-casual dining and the cuisine of owner Mark Sy's childhood, Viên Restaurant offers a make-your-own meal setup—like Chipotle, but with rice noodles and lemon grass chicken instead of black beans and carnitas.

"When I came to New York in 2011, I saw similar concepts, but no one was doing it with Southeast Asian food," says Mr. Sy. "I grew up in Hong Kong and the Philippines, so I wanted to offer a variety of dishes that I loved from those countries instead of just sticking to one."